2015/08/28 by Rademacher, Christine, Rademacher, Hans-Bert
#34A05 #34A30 (Secondary) #53C44 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1508.07274
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called (affine) soliton of the transformation T if its image under T is an affine image of the polygon. We describe a large class of solitons by considering smooth curves which are solutions of a linear system of differential equations of second order with constant coefficients. As examples we obtain solitons lying on spiral curves which under the transformation T rotate and shrink.